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In [[probability theory]], a ''cumulative distribution function''  ''F(x)'' of a [[probability density function]] say ''f(x)'' is a real valued and continuous function whose value is the proportion of probability values of a variable which occur on the part real line up and including the value of that variable; i.e.,
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In [[probability theory]], a ''cumulative distribution function''  ''F(x)'' of a [[probability density function]] say ''f(x)'' is a real valued and continuous function whose value is the proportion of probability values of a variable which occur on the part of the real line up and including the value of that variable; i.e.,
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(2) <math> F(\infty) = 1 </math>,  i.e., finitely convergent (to unity by convention).
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(2) <math> \lim_{x \to \infty}F(x) = 1 </math>,  i.e., finitely convergent (to unity by convention).
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If the [[domain]] of the variable is [[finite]], then the argument in equation (2) above should be the upper bounds.
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If the [[domain]] of the variable is [[finite]], then the upper limit equation (2) above should be the upper bound.
       
[[Category:mathematics]]
 
[[Category:mathematics]]
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